English

Commensurability of automorphism groups

Rings and Algebras 2019-02-20 v2 Number Theory

Abstract

We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra heuristics on class groups. The number theoretic implications will be addressed in a separate paper.

Keywords

Cite

@article{arxiv.1510.02758,
  title  = {Commensurability of automorphism groups},
  author = {Alex Bartel and Hendrik W. Lenstra},
  journal= {arXiv preprint arXiv:1510.02758},
  year   = {2019}
}

Comments

26 pages; improved the introduction and the exposition in the body of the paper. The final version is to appear in Compositio Math

R2 v1 2026-06-22T11:16:46.890Z